Mass flow measurement methods, apparatus, and computer program products using mode selective filtering

ABSTRACT

Mass flow of a material in a conduit is estimated by mode selective filtering a plurality of motion signals representing motion of the conduit to generate a plurality of mode selective filtered motion signals such that the mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the conduit. A plurality of phase estimates is generated from the plurality of mode selective filtered motion signals. A mass flow estimate is generated from the plurality of phase estimates. The plurality of phase estimates may be estimated using a phase reference derived from one of the plurality of mode selective filtered motion signals. In some embodiments, a frequency of a mode selective filtered motion signal of the plurality of mode selective filtered motion signals is estimated. Quadrature first and second reference signals are generated based on the estimated frequency. The plurality of phase estimates is generated from the plurality of mode selective filtered motion signals and the first and second reference signals. A plurality of time difference estimates may be generated from the plurality of phase estimates, and the mass flow estimate may be generated from the plurality of time difference estimates. The plurality of time difference estimates may be generated from the plurality of phase estimates by dividing the plurality of phase estimates using a mode frequency estimated from the mode selective filtered motion signals. The invention may be embodied as methods, apparatus and computer program products.

FIELD OF THE INVENTION

The present invention relates to sensors and related methods andcomputer program products, and more particularly, to mass flowmeasurement methods, apparatus, computer program products.

BACKGROUND OF THE INVENTION

Many sensor applications involve the detection of mechanical vibrationor other motion. Examples of sensors that utilize such motion detectioninclude Coriolis mass flowmeters and vibrating tube densitometers. Thesedevices typically include a conduit or other vessel that is periodicallydriven, i.e., vibrated. Properties such as mass flow, density and thelike associated with a material contained in the conduit or vessel maybe determined by processing signals from motion transducers positionedon the containment structure, as the vibrational modes of the vibratingmaterial-filled system generally are affected by the combined mass,stiffness and damping characteristics of the containing conduit orvessel structure and the material contained therein.

A typical Coriolis mass flowmeter includes one or more conduits that areconnected inline in a pipeline or other transport system and conveymaterial, e.g., fluids, slurries and the like, in the system. Eachconduit may be viewed as having a set of natural vibrational modesincluding, for example, simple bending, torsional, radial and coupledmodes. In a typical Coriolis mass flow measurement application, aconduit is excited at resonance in one of its natural vibrational modesas a material flows through the conduit, and motion of the conduit ismeasured at points along the conduit. Excitation is typically providedby an actuator, e.g., an electromechanical device, such as a voicecoil-type driver, that perturbs the conduit in a periodic fashion.Exemplary Coriolis mass flowmeters are described in U.S. Pat. Nos.4,109,524 to Smith, 4,491,025 to Smith et al., and Re. 31,450 to Smith.

Unfortunately, the accuracy of conventional Coriolis mass flowmeters maybe compromised by nonlinearities and asymmetries in the conduitstructure, motion arising from extraneous forces, such as forcesgenerated by pumps and compressors that are attached to the flowmeter,and motion arising from pressure forces exerted by the material flowingthrough the flowmeter conduit. The effects of these forces are commonlyreduced for by using flowmeter designs that are balanced to reduceeffects attributable to external vibration, and by using frequencydomain filters, e.g., bandpass filters designed to filter out componentsof the motion signals away from the excitation frequency. However,mechanical filtering approaches are often limited by mechanicalconsiderations, e.g., material limitations, mounting constraints, weightlimitations, size limitations and the like, and frequency domainfiltering may be ineffective at removing unwanted vibrationalcontributions near the excitation frequency.

SUMMARY OF THE INVENTION

According to embodiments of the invention, mass flow of a material in aconduit is estimated by mode selective filtering a plurality of motionsignals representing motion of the conduit to generate a plurality ofmode selective filtered motion signals such that the mode selectivefiltered motion signals preferentially represent motion associated witha vibrational mode of the conduit. A plurality of phase estimates isgenerated from the plurality of mode selective filtered motion signals.A mass flow estimate is generated from the plurality of phase estimates.The plurality of phase estimates may be estimated using a phasereference derived from one of the plurality of mode selective filteredmotion signals.

In some embodiments of the invention, a modal transformation is appliedto the plurality of motion signals to generate a plurality of modalresponse signals in a modal coordinate domain. A mode selectivetransformation is applied to the plurality of modal response signals togenerate the plurality of mode selective filtered motion signals. Inother embodiments of the invention, a frequency of a mode selectivefiltered motion signal of the plurality of mode selective filteredmotion signals is estimated. Quadrature first and second referencesignals are generated based on the estimated frequency. The plurality ofphase estimates is generated from the plurality of mode selectivefiltered motion signals and the first and second reference signals.

In still other embodiments of the invention, a plurality of timedifference estimates is generated from the plurality of phase estimates,and the mass flow estimate is generated from the plurality of timedifference estimates. The plurality of time difference estimates may begenerated from the plurality of phase estimates by dividing theplurality of phase estimates by a mode frequency to generate a pluralityof time difference values. A plurality of zero-flow reference timedifferences may be applied to the plurality of time difference values togenerate the plurality of time difference estimates. The mode frequencymay be estimated from a modal motion signal generated from the pluralityof motion signals. Density of material in the conduit may also beestimated from the estimated mode frequency.

According to other aspects of the invention, mass flow of a material ina conduit may be determined by processing a plurality of motion signalsrepresenting motion of the conduit using one of the plurality of motionsignals as a timing reference to generate a like plurality of differenceestimates, and estimating a slope parameter of a scaling function thatrelates the plurality of difference estimates to a like plurality ofreference differences representing motion of the conduit at a known massflow. A mass flow estimate may be estimated from the estimated slopeparameter and the known mass flow.

In some embodiments of the invention, an augmented matrix including theplurality of reference differences is generated. The plurality ofdifference estimates is multiplied by a pseudoinverse of the augmentedmatrix to determine the slope parameter. In other embodiments, theplurality of difference estimates is multiplied by a pseudoinverse ofthe reference time differences to determine the slope parameter. Thescaling parameter can also be iteratively estimated to determine theslope parameter, using, for example, a Least Mean Square (LMS)estimation procedure.

According to other aspects of the invention, an apparatus includes aconduit configured to contain a material. A plurality of motiontransducers is operatively associated with the conduit and operative toproduce a plurality of motion signals representing motion of theconduit. A signal processing circuit receives the plurality of motionsignals and mode selective filters the plurality of motion signals togenerate a plurality of mode selective filtered motion signals such thatthe mode selective filtered motion signals preferentially representmotion associated with a vibrational mode of the conduit. The signalprocessing circuit generates a plurality of phase estimates from theplurality of mode selective filtered motion signals, and generates amass flow estimate from the plurality of phase estimates. The signalprocessing circuit may generate the plurality of phase estimates using aphase reference derived from one of the plurality of mode selectivefiltered motion signals.

According to still other embodiments of the invention, an apparatusincludes a conduit and a plurality of motion transducers, operativelyassociated with the conduit, that generate a plurality of motion signalsrepresenting motion of the conduit. A signal processing circuit receivesthe plurality of motion signals and processes the plurality of motionsignals using one of the plurality of motion signals as a timingreference to generate a like plurality of difference estimates. Thesignal processing circuit estimates a slope parameter of a scalingfunction that relates the plurality of difference estimates to a likeplurality of reference differences representing motion of the conduit ata known mass flow, and generates a mass flow estimate from the estimatedslope parameter and the known mass flow. The signal processing circuitmay generate an augmented matrix including the plurality of referencedifferences, and may multiply the plurality of difference estimates by apseudoinverse of the augmented matrix to determine the slope parameter.Alternatively, the signal processing circuit may multiply the pluralityof difference estimates by a pseudoinverse of the reference timedifferences to determine the slope parameter. The signal processing mayalso iteratively estimate the scaling function.

According to other aspects of the invention, a computer program productfor estimating mass flow of a material in a conduit includes acomputer-readable storage medium having computer-readable program codeembodied in the computer-readable storage medium. The computer-readableprogram code includes mass flow estimating computer-readable programcode that mode selective filters a plurality of motion signalsrepresenting motion of the conduit to generate a plurality of modeselective filtered motion signals such that the mode selective filteredmotion signals preferentially represent motion associated with avibrational mode of the conduit, that generates a plurality of phaseestimates from the plurality of mode selective filtered motion signals,and that generates a mass flow estimate from the plurality of phaseestimates. The mass-flow estimating computer-readable program code maygenerate the plurality of phase estimates using a phase referencederived from one of the plurality of mode selective filtered motionsignals. For example, the mass flow estimating computer-readable programcode may estimate a frequency of a mode selective filtered motion signalof the plurality of mode selective filtered motion signals, generatequadrature first and second reference signals based on the estimatedfrequency, and generate the plurality of phase estimates from theplurality of mode selective filtered motion signals and the first andsecond reference signals.

According to other embodiments, the mass flow estimatingcomputer-readable program code generates a plurality of time differenceestimates from the plurality of phase estimates and generates the massflow estimate from the plurality of time difference estimates. The massflow estimating computer-readable program code may apply a modaltransformation to the plurality of motion signals to generate a modalmotion signal in a modal coordinate domain, estimate a mode frequencyfrom the modal motion signal, and generate the plurality of timedifference estimates from the plurality of phase estimates using theestimated mode frequency. The computer-readable program code may furtherinclude density estimating computer program code that estimates densityof material in the conduit from the estimated mode frequency.

According to yet other aspects of the invention, computer-readableprogram code embodied in a computer-readable storage medium includesmass flow estimating computer-readable program code that processes aplurality of motion signals representing motion of the conduit using oneof the plurality of motion signals as a timing reference to generate alike plurality of difference estimates, that estimates a slope parameterof a scaling function that relates the plurality of difference estimatesto a like plurality of reference differences representing motion of theconduit at a known mass flow, and that generates a mass flow estimatefrom the estimated slope parameter and the known mass flow. The massflow estimating computer-readable program code may generate an augmentedmatrix including the plurality of reference differences and multiply theplurality of difference estimates by a pseudoinverse of the augmentedmatrix to determine the slope parameter. Alternatively, the mass flowestimating computer-readable program code may multiply the plurality ofdifference estimates by a pseudoinverse of the reference timedifferences to determine the slope parameter. The mass flow estimatingcomputer-readable program code may also iteratively estimate the scalingfunction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram conceptually illustrating a curved-tubeflow sensor structure.

FIG. 2 is a schematic diagram conceptually illustrating a straight-tubeflow sensor structure.

FIG. 3 is a schematic diagram illustrating a mass flow estimatingapparatus according to embodiments of the invention.

FIG. 4 is a schematic diagram illustrating a signal processing circuitaccording to other embodiments of the invention.

FIG. 5 is a schematic diagram illustrating a mass flow estimatingapparatus according to other embodiments of the invention.

FIG. 6 is a schematic diagram illustrating an apparatus for estimatingmass flow and density according to embodiments of the invention.

FIG. 7 is a schematic diagram illustrating an apparatus for generatingphase estimates according to embodiments of the invention.

FIG. 8 is a schematic diagram illustrating an apparatus for generatingphase estimates according to other embodiments of the invention.

FIG. 9 is a schematic diagram illustrating an apparatus for generatingtime difference estimates according to embodiments of the invention.

FIG. 10 is a flowchart illustrating operations for estimating mass flowaccording to embodiments of the invention.

FIG. 11 is a flowchart illustrating operations for estimating mass flowaccording to other embodiments of the invention.

FIGS. 12 and 13 are waveform diagrams illustrating mass flow estimationoperations according to the invention.

FIG. 14 is a flowchart illustrating operations for iterativelyestimating a mass flow scaling vector according to embodiments of thepresent invention.

FIG. 15 is a flowchart illustrating operations for generating phaseestimates according to embodiments of the invention.

FIG. 16 is a flowchart illustrating operations for estimating mass flowaccording to other embodiments of the invention.

FIG. 17 is a flowchart illustrating operations for generating differenceestimates according to embodiments of the invention.

FIG. 18 is a flowchart illustrating operations for estimating mass flowaccording to embodiments of the invention.

FIG. 19 is a flowchart illustrating operations for estimating densityaccording to embodiments of the invention.

FIGS. 20A, 20B and 21-27 are waveform diagrams illustrating exemplaryeffects of system changes according to aspects of the invention.

FIGS. 28-30 are flowcharts illustrating operations for monitoring systemstatus and compensating for system changes according to embodiments ofthe invention.

DETAILED DESCRIPTION OF EMBODIMENTS

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout. As will be appreciated by oneof skill in the art, the present invention may be embodied as systems(apparatus), methods, or computer program products.

The embodiments of the present invention described herein relate toCoriolis mass flowmeters. Those skilled in the art will appreciate,however, that the invention described herein is generally applicable todetermination of motion in a wide variety of mechanical structures, andthus the apparatus and methods of the present invention are not limitedto Coriolis mass flowmetering.

As will be appreciated by one of skill in the art, the present inventionmay be embodied as apparatus and/or method and/or computer programproduct. Accordingly, the present invention may be implemented inhardware or in a combination of hardware and software aspects.Furthermore, the present invention may also take the form of a computerprogram product including a computer-usable storage medium havingcomputer-usable program code embodied in the medium. Any suitablecomputer readable medium may be utilized, including semiconductor memorydevices (e.g., RAMs, ROMs, EEPROMs, and the like), hard disks, CD-ROMs,optical storage devices, and magnetic storage devices.

Computer program code for carrying out operations of the presentinvention may be written in an object oriented programming language,such as Java® or C++, and/or in a procedural programming languages, suchas “C.” The program code may execute one a single computer or dataprocessing device, such as a microcontroller, microprocessor, or digitalsignal processor (DSP), or may be executed on multiple devices, forexample, on multiple data processing devices that communicate via serialor parallel data busses within an electronic circuit board, chassis orassembly, or which form part of a data communications network such as alocal area network (LAN), wide area network (WAN), or internet.

The present invention is described below with reference to flowchartillustrations and/or block diagrams of methods, apparatus (systems) andcomputer program products according to embodiments of the invention. Itwill be understood that each block of the flowchart illustrations and/orblock diagrams, and combinations of blocks in the flowchartillustrations and/or block diagrams, can be implemented by computerprogram code (instructions). These computer program code may be providedto a processor of a general purpose computer, special purpose computer,or other programmable data processing apparatus to produce a machine,such that the instructions, which execute via the processor of thecomputer or other programmable data processing apparatus, create meansfor implementing the functions specified in the flowchart and/or blockdiagram block or blocks.

These computer program products also may be embodied in acomputer-readable storage medium (e.g., magnetic disk or semiconductormemory, code magnetic memory or the like) that can direct a computer orother programmable data processing apparatus to function in a particularmanner, such that the computer program stored in the computer-readablememory produce an article of manufacture including instruction meanswhich implement the function specified in the flowchart and/or blockdiagram block or blocks.

The computer program code may also be loaded onto a computer or otherprogrammable data processing apparatus to cause a series of operationalsteps to be performed on the computer or other programmable apparatus toproduce a computer implemented process such that the code that executeson the computer or other programmable apparatus provides steps forimplementing the functions specified in the flowchart and/or blockdiagram block or blocks.

Modal Behavior of a Vibrating Conduit

Behavior of a vibrating structure such as a Coriolis mass flowmeterconduit may be described in terms of one or more natural modes havingassociated natural frequencies of vibration. The modes and theassociated natural frequencies may be mathematically described byeigenvectors and associated eigenvalues, the eigenvectors being uniquein relative magnitude but not absolute magnitude and orthogonal withrespect to the mass and stiffness of the structure. The linearlyindependent set of vectors may be used as a transformation to uncoupleequations that describe the structure's motion. In particular, theresponse of the structure to an excitation can be represented as asuperposition of scaled modes, the scaling representing the contributionof each mode to the motion of the structure. Depending on theexcitation, some modes may contribute more than others. Some modes maybe undesirable because they may contribute energy at the resonantfrequency of desired modes and, therefore, may corrupt measurementstaken at the resonant frequency of a desired mode, such as phasedifference measurements taken at the drive frequency.

Conventional Coriolis mass flowmeters typically use structural andtemporal filtering to reduce the effects of undesirable modes.Conventional structural filtering techniques include using mechanicalfeatures such as brace bars designed to decouple in phase and out ofphase bending modes, actuators positioned such that they are less likelyto excite undesirable modes, and transducers positioned such that theyare less sensitive to undesirable modes. Structural filtering techniquescan be very effective in reducing energy of undesired modes, but may belimited by geometric and fabrication constraints.

Temporal filtering techniques typically modify transducer signals basedon time domain or frequency domain parameters. For example, a typicalCoriolis mass flowmeter may include frequency domain filters designed toremove frequency components that are significantly correlated withundesired modes. However, off-resonance energy from undesired modes maycontribute considerably to energy at the resonant frequency of a desiredmode. Because frequency-domain filters generally are ineffective atdistinguishing the contribution of multiple modes at a given frequency,the contribution of undesired modes at a measurement frequency may be asignificant source of error in process parameter measurements.

A sensor conduit structure with negligible damping and zero flow may beassumed to have purely real natural or normal modes of vibration, i.e.,in each mode, each point of the structure reaches maximum differencesimultaneously. However, a real conduit having non-negligible dampingand a material flowing therethrough has a generally complex response toexcitation, i.e., points of the structure generally do notsimultaneously reach maximum amplitude. The motion of the conduitstructure may be described as a complex mode having real and imaginarycomponents or, alternatively, magnitude and phase components. Coriolisforces imparted by the flowing material render motion of the sensorconduit mathematically complex.

Even if complex, motion of a conduit structure can be described as asuperposition of scaled natural (“normal” or “single degree of freedom”(SDOF)) modes, as the real and imaginary parts of a complex mode arelinearly independent by definition. To represent complex motion, complexscaling coefficients may be used in combining the constituent realnormal modes. Particular real normal modes may be closely correlatedwith the imaginary component of the complex mode while beingsignificantly less correlated with the real component of the complexmode. Accordingly, these particular real normal modes may be moreclosely correlated with the Coriolis forces associated with the materialin the sensor conduit, and thus can provide information for generatingan accurate estimate of a parameter associated with the material.

A conceptual model of one type of Coriolis mass flowmeter sensor 100 isprovided in FIG. 1. Motion transducers 105A, 105B, 105C, 105D (e.g.,velocity transducers) are positioned to detect relative motion of firstand second curved conduits 103A, 103B of the sensor 100 that arevibrated by a an actuator 106 as a material 108 flows through theconduits 103A, 103B, the motion transducers 105A, 105B, 105C, 105Dproducing motion signals 109. A “straight tube” Coriolis flowmetersensor 200 illustrated in FIG. 2 includes a conduit 203 configured tocontain a material 208 from a pipeline 207 connected to the sensor 200at flanges 202. Within a housing 204 surrounding the conduit 203, anactuator 206 is operative to excite the conduit 203. Motion transducers205A, 205B, 205C, 205D (e.g., velocity transducers, accelerometers orother motion-sensing devices) are positioned along the conduit 203. Themotion transducers 205A, 205B, 205C, 205D produce motion signals 209representing motion of the conduit 203 in response to a plurality offorces F that may include, for example, a drive force imparted by theactuator 206, Coriolis forces arising from the flowing material 208,pressure forces exerted by the material 208, and other extraneous forcessuch as forces imparted by the pipeline 207 and forces generated bypumps, compressors and other equipment (not shown) connected to thepipeline 207 and conveyed to the conduit 203 via the flanges 202.

For a flowmeter structure such as those illustrated in FIGS. 1 and 2, aresponse vector x can be constructed from the signals produced by motiontransducers that are operatively associated with the structure, such asthe motion signals 109, 209 produced by motion transducers 105A, 105B,105C, 105D, 205A, 205B, 205C, 205D of FIGS. 1 and 2. For example, themotion signals may be sampled to generate motion signal values x₁, x₂, .. . , x_(n) of a response vector x. A real normal modal matrix Φ, thatis, an eigenvector matrix relating the physical motion vector to a modalmotion vector η representing motion in a plurality of natural (SDOF)modes, may then be identified such that:

x=Öç.  (1)

The modal matrix Φ can be identified using a number of techniques. Forexample, trial and error or inverse techniques may be used as describedin U.S. Pat. Application Ser. No. 08/890,785, filed Jul. 11, 1997,assigned to the assignee of the present application and incorporated byreference herein in its entirety.

Exemplary Mass Flowmeters

According to embodiments of the present invention, selective modalfiltering techniques are used to produce mode selective filtered motionsignals that are then used to generate phase estimates, which are inturn used to generate a mass flow estimate. Exemplary embodimentsaccording to this aspect of the present invention will now be described,in particular, embodiments using “straight tube” sensors such as thesensor 200 of FIG. 2. Those skilled in the art will appreciate, however,that the present invention is also applicable to curved-conduitstructures, such as that used in the sensor 100 illustrated in FIG. 1,as well as to other material-containing structures used in massflowmeters, densitometers and the like. Those skilled in the art willfurther appreciate that the present invention is also applicable to thecharacterization of motion in a variety of other structures.

FIG. 3 illustrates a mass flow estimating apparatus 300 according toembodiments of the present invention. The apparatus 300 includes amaterial-containing conduit 203 and operatively associated motiontransducers 205A, 205B, 205C, 205D of a flowmeter sensor 200, along witha signal processing circuit 301 that is operative to generate a massflow estimate from motion signals 305 produced by the motion transducers205A, 205B, 205C, 205D. Like numbers are used in FIGS. 2 and 3 to denotelike components of the sensor 200, detailed description of which willnot be repeated here in light of the description of FIG. 2.

The signal processing circuit 301 includes a mode selective filter 310that is configured to receive the motion signals 305 and operative toselectively pass one or more components of the motion signals 305 toproduce a plurality of mode selective filtered motion signals 315. Themode selective filter 310 is preferably derived from a modalcharacterization of the sensor 200 as described in U.S. patentapplication Ser. No. 09/116,410, filed Jul. 16, 1998 the disclosure ofwhich is incorporated by reference herein in its entirety. The signalprocessing circuit 301 also includes a phase estimator 320 that isresponsive to the mode selective filtered motion signals 315 andoperative to generate a plurality of phase estimates 325 therefrom. Thesignal processing circuit 301 further includes a mass flow estimator 330that is responsive to the phase estimator 320 and produces a mass flowestimate 335 from the plurality of phase estimates 325.

FIG. 4 illustrates an exemplary implementation of a mode selectivefilter 410, phase estimator 420 and mass flow estimator 430 according toembodiments of the present invention. A plurality of motion signals 405a, e.g., analog outputs from velocity or other motion transducersoperatively associated with a conduit or other material-containingvessel, is sampled and digitized by an AID converter 440, producing aplurality of digital motion signals 405 b. The digital motion signals405 b are processed by a digital mode selective filter 410 to produce aplurality of mode selective filtered digital motion signals 415. Adigital phase estimator 420 generates a plurality of digital phaseestimates 425 from the plurality of mode selective filtered digitalmotion signals 415. A digital mass flow estimator 430 produces a digitalmass flow estimate 435 from the plurality of digital phase estimates425. As shown, the mode selective filter 410, the phase estimator 420and the mass flow estimator 430 may be implemented as computer readableprogram code executed by a data processor 450, for example, acombination of a computer (e.g., a microcontroller, microprocessor,digital signal processor (DSP), or other computing device) and anassociated storage medium (e.g., semiconductor memory magnetic storageand/or optical storage).

FIG. 5 illustrates an exemplary mass flow estimating apparatus 500according to other embodiments of the present invention. The apparatus500 includes a material-containing conduit 203 and operativelyassociated motion transducers 205A, 205B, 205C, 205D of a straight-tubesensor 200 such as that described with reference to FIG. 2, furtherdetailed description of which will not be repeated in light of thedescription of FIG. 2. A signal processing circuit 501 includes a modeselective filter 510 that is configured to receive the motion signals505 produced by the sensor 200 and operative to selectively pass one ormore components of the motion signals 505 to produce a plurality of modeselective filtered motion signals 515. The mode selective filter 510 isfurther operative to produce at least one modal motion signal 517, i.e.,at least one signal that represents motion of the conduit 203 in a modaldomain defined by at least one natural (SDOF) mode of the conduit 203.The mode selective filter 510 is preferably derived from a modalcharacterization of the sensor 200 as described in the aforementionedU.S. patent application Ser. No. 09/116,410, filed Jul. 16, 1998.

The signal processing circuit 501 further includes a phase estimator 520that is responsive to the mode selective filter 510 and operative togenerate a plurality of phase estimates 525 from the plurality of modeselective filtered motion signals 515. The signal processing circuit 501also includes a mass flow estimator 530 that is responsive to the phaseestimator 520 and produces a mass flow estimate 535 from the pluralityof phase estimates 525 using at least one mode frequency estimate 545generated by a mode frequency estimator 540. The mode frequencyestimator 540 produces the at least one mode frequency estimate 545responsive to the at least one modal motion signal 517. The signalprocessing circuit 501 further includes a density estimator 550 that isresponsive to the at least one mode frequency estimate 545 to generate adensity estimate 555.

FIG. 6 illustrates an apparatus 600 operative to estimate mass flow anddensity from a plurality of motion signals 605, according to embodimentsof the invention. The apparatus 600 includes a mode selective filter610, a phase estimator 620, a mass flow estimator 630, a mode frequencyestimator 640 and a density estimator 650. The mode selective (or “modepass”) filter 610 includes a modal transformation 612 that transforms aplurality of motion signals 605 into a plurality of modal motion signals613 that represent motion in a plurality of natural modes, as describedabove with reference to equation (1) and in the aforementioned U.S.patent application Ser. No. 09/116,410, filed Jul. 16, 1998. The modeselective filter 610 also includes a mode selective transformation 614that selectively transforms the plurality of modal motion signals 613back out of the modal domain, producing mode selective filtered motionsignals 615 that are filtered such that components of the originalmotion signals 615 that are associated with one or more desired modesare preferentially passed in relation to components associated withother, undesired natural modes. Such a mode selective transformation isalso described in U.S. patent application Ser. No. 09/116,410, filedJul. 16, 1998. The modal motion signals 613 are passed on to the modefrequency estimator 640, which generates one or more mode frequencyestimates 645.

The mode selective filtered motion signals 615 are passed on to thephase estimator 620, which generates a plurality of phase estimates 625therefrom using a phase reference that is derived from the plurality ofmotion signals 605. For example, as described in detail with referenceto FIG. 7 below, the phase reference may be derived from one or more ofthe mode selective filtered motion signals 615. Alternatively, the phasereference may be derived from one or more mode frequency estimates 645generated from one or more of the modal motion signals 613 by the modefrequency estimator 640.

The phase estimates 625 are passed onto the mass flow estimator 630 thatincludes a time difference estimator 632 and a spatial integrator 634.Using the one or more mode frequency estimates 645 generated by the modefrequency estimator 640, the time difference estimator 632 generates aplurality of time difference estimates 633 from the plurality of phaseestimates 625. The time difference estimator 640 may also use zero-flowreference time differences 631, i.e., values representing timedifferences under a zero mass flow condition which may corruptmeasurements at other mass flow rates, to generate time differences 633that are corrected for such “zero offset.” As described below, anestimate of a drive mode frequency may be generated by the modefrequency estimator 640, and phase estimates may be divided by thisestimated drive mode frequency to yield uncorrected time differenceestimates. The uncorrected time difference estimates may then becorrected using the zero-flow reference time differences 631 (e.g., bysubtraction therefrom) to generate the time difference estimates 633.

The time difference estimates 633 generated by the time differenceestimator 632 are provided to a spatial integrator 634. As described indetail below, the spatial integrator 634 may determine a slope parameterof a scaling vector function that relates the plurality of timedifference estimates 633 to a plurality reference time differences 637corresponding to a known mass flow. This slope parameter may then beused to generate a mass flow estimate 635 from the known mass flow.

As also shown in FIG. 6, the density estimator 650 may also use the modefrequency estimate 645 to generate an estimate of density of thematerial for which mass flow is being determined. The density estimator650 may utilize techniques similar to those used to generate a densityestimate 655 from a non-mode selective filtered transducer signal, suchas those described in U.S. Pat. No. 5,687,100 to Buttler et al (issuedNov. 11, 1997) and U.S. Pat. No. 5,295,084 to Arunachalam et al. (issuedMar. 15, 1994), incorporated by reference herein in their entireties.For example, according to embodiments of the present invention, densityestimates may be generated by using modal frequency estimates in placeof the conventional frequency estimates utilized in the aforementionedpatents.

FIGS. 7-9 illustrate exemplary structures for implementing variouscomponents of FIG. 6. It will be appreciated that the mode selectivefilter 610, phase estimator 620, mass flow estimator 630, the modefrequency estimator 640 of FIG. 6, as well as the structures of FIGS.7-9, may be implemented in a digital domain, e.g., as executablemodules, subroutines, objects and/or other types of software and/orfirmware running on a microprocessor, microcontroller, DSP or othercomputing device. In such implementations, “signals,” such as the modalmotion signals 613, mode selective filtered motion signals 615 and phaseestimates 633 may include vectors of digital signal values that areproduced at calculation intervals and upon which computations areperformed to implement the functions described. However, it will beappreciated that all or some of these signals may, in general, bedigital or analog, and that the operations performed thereon may beperformed by special-purpose digital hardware and/or analogous analoghardware.

FIG. 7 illustrates an example of a phase estimator 700 according toembodiments of the present invention. The phase estimator 700 includes afrequency estimator 710 that estimates a frequency of a mode selectivefiltered motion signal 701 ₁ of a plurality of mode selective filteredmotion signals 701 ₁, 701 ₂, . . . 701 _(n). The frequency estimator 710produces a frequency estimate 715 which is applied to a quadraturereference signal generator 720 that generates first and second (e.g.,sine and cosine) reference signals 725 a, 725 b that have the estimatedfrequency and that are in phase quadrature with respect to one another.The frequency estimator 710 may, for example, be a digitally-implementedadaptive notch filter that is operative to determine the frequencyestimate 715, and the quadrature reference signal generator 720 maygenerate the quadrature reference signals 725 a, 725 b using a “twiddle”function, in a manner similar to that described in U.S. patentapplication Ser. No. 09/344,840 entitled Multi-Rate Digital SignalProcessor for Signals from Pick-Offs on a Vibrating Conduit, filed Jun.28, 1999, assigned to the assignee of the present invention, andincorporated herein by reference in its entirety. However, it will beappreciated that other techniques, including other digital and analogsignal processing techniques for generating phase and quadraturereference signals, may be used to generate the frequency estimate 715and/or the quadrature reference signals 725 a, 725 b. For example,rather than generating the frequency estimate 715 from amode-selectively filtered signal as shown in FIG. 7, the frequencyestimate may be a mode frequency estimate, such as one or more of themode frequency estimates 645 produced by the mode frequency estimator640 of FIG. 6.

The first and second phase reference signals 725 a, 725 b are applied toa plurality of phase calculators 730 ₁, 730 ₂, . . . , 730 _(n),respective ones of which generate respective phase estimates 735 ₁, 735₂, . . . 735 _(n) from respective ones of the mode selective filteredmotion signals 701 ₁, 701 ₂, . . . , 701 _(n). Phase estimates 735 ₂, .. . , 735 _(n) are then normalized with respect to one of the phaseestimates phase estimates 735 ₁ by a normalizer 740 to produce aplurality of normalized phase estimates 745 ₁, 745 ₂, . . . , 745 _(n).The normalized phase estimates 745 ₁, 745 ₂, . . . , 745 _(n) may thenbe used to estimate mass flow, as described above with reference to FIG.6.

Referring again to FIG. 6, the mode frequency estimator 640 may usefrequency estimation techniques similar to those described above withreference to FIG. 7. For example, the frequency-determining adaptivenotch filtering techniques described in the aforementioned U.S. patentapplication Ser. No. 09/344,840 entitled Multi-Rate Digital SignalProcessor for Signals from Pick-Offs on a Vibrating Conduit may be usedto generate at least one frequency estimate 645 for at least one of themodal motion signals 617.

Exemplary computing operations for demodulating a mode selectivefiltered motion signal 701 j using the synthesized quadrature (e.g.,sine and cosine) reference signals 725 a, 725 b are illustrated in FIG.8. The mode selective filtered motion signal 701 j is separatelymultiplied by each of the quadrature reference signals 725 a, 725 b,generating real and imaginary component signals 805 b, 805 a. Anarctangent calculator 810 then computes an arctangent of the real andimaginary component signals 805 b, 805 a to generate a phase estimate735 j. Preferably, the real and imaginary component signals 805 b, 805 aare filtered before application to the arctangent calculator 810, suchthat non-DC components of the signals 805 b, 805 a are attenuated.

FIG. 9 illustrates an exemplary computing structure for generatingcorrected time difference estimates 633 according to embodiments of thepresent invention. A vector of phase estimates 625 (which may benormalized) is divided by an estimated mode frequency 645, preferablyone or more frequencies associated with a drive mode. The resultingvector of time differences 915 is then corrected by subtracting acorresponding vector of zero-flow reference time differences 631,producing a vector of corrected time difference estimates 633. A similarcorrection could alternatively be achieved by subtracting a vector ofphase values associated with zero flow from the phase estimates 735 ₁,735 ₂, . . . , 735 _(n) described above.

Spatial Integration of Time Difference Estimates

According to other aspects of the present invention, time differencesestimates, such as the corrected time difference estimates describedabove, may be processed using a “spatial integration” procedure toproduce a mass flow estimate. According to various embodiments of thepresent invention described below, numerous techniques may be used todetermine a slope parameter that relates time difference estimatesassociated with an unknown mass flow to reference time differencesassociated with a known mass flow, including closed-form pseudoinversetechniques and iterative techniques. This slope parameter may be used togenerate an estimate of the unknown mass flow.

As described in the aforementioned U.S. patent application Ser. No.09/116,410, filed Jul. 16, 1998, a vector Y_(e) of time differencevalues at known mass flow F_(c) may be identified, and an unknown massflow can be described in terms of this reference time difference vectorY_(e) by a scalar multiplication, that is, a vector of estimated timedifferences X_(e) for an unknown mass flow can be scaled by a scalefactor a (hereinafter referred to as a “slope parameter”) to produce thereference time difference vector Y_(e). In order to determine theunknown mass flow, the known mass flow F_(c) is multiplied by the slopeparameter a. The reference time difference vector Y_(e) and the timedifference estimate vector X_(e) may be related as:

$\begin{matrix}{X_{e} = {{aY}_{e} + {b{{\begin{matrix}{RU} \\{SV} \\{TW}\end{matrix}}.}}}} & (2)\end{matrix}$

Rearranging equation (2) gives:

$\begin{matrix}{{X_{e} = {{\begin{bmatrix}\quad & 1 \\Y_{e} & \vdots \\\quad & 1\end{bmatrix}\begin{Bmatrix}a \\b\end{Bmatrix}} = {Zc}}},} & (3)\end{matrix}$

where the augmented matrix Z is formed by augmenting the reference timedifference vector Y_(e) with a column of ones. Equation (3) may besolved for the scaling vector c by premultiplying the time differenceestimate vector X_(e) by the pseudo inverse W of the augmented matrix Z:

c=Z ⁻ X _(e) =WX _(e),  (4)

where the matrix inverse operator (⁻¹) is used to denote a pseudoinverse. Solving for the vector c and then multiplying F_(c) by theslope parameter a of the vector c can yield an estimate of mass flow.

FIGS. 10 and 11 are flowchart illustrations of exemplary operations forgenerating a mass flow estimate from a plurality of time differenceestimates according to various embodiments of the present invention.Those skilled in the art will understand that the operations of theseflowchart illustrations may be can be implemented using computerinstructions. These instructions may be executed on a computer or otherdata processing apparatus, such as the data processor 450 of FIG. 4, tocreate an apparatus (system) operative to perform the illustratedoperations. The computer instructions may also be stored as computerreadable program code on a computer readable medium, for example, anintegrated circuit memory, a magnetic disk, a tape or the like, that candirect a computer or other data processing apparatus to perform theillustrated operations, thus providing means for performing theillustrated operations. The computer readable program code may also beexecuted on a computer or other data-processing apparatus to cause theapparatus to perform a computer-implemented process. Accordingly, FIGS.10 and 11 support apparatus (systems), computer program products andmethods for performing the operations illustrated therein.

FIG. 10 illustrates operations 1000 for generating a mass flow estimatefrom a vector X_(e) of time difference estimates along theabove-described lines according to embodiments of the present invention.A pseudoinverse W of an augmented matrix Z including a vector ofreference time differences Y_(e) associated with a known mass flow F_(c)augmented by a column of ones is determined (Block 1010). Thedetermination of the augmented matrix Z and the pseudoinverse matrix Wmay be done on an intermittent basis, e.g., at calibration, to reducecomputational burdens. The vector of time difference estimates X_(e) ismultiplied by the pseudoinverse matrix W, to produce a scaling vector c,including a slope parameter a and an intercept parameter b (Block 1020).The slope parameter a is then multiplied by the known mass flow F_(c) toproduce a mass flow estimate (Block 1030). It will be appreciated thatthe mass flow estimate may be further processed; for example, the massflow estimate may be averaged with other mass flow estimates determinedover a time period to produce a filtered mass flow measurement (Block1040). The intercept parameter b may also be monitored, for example, todetect system changes (Block 1050).

There are several advantages to monitoring the intercept parameter b ofthe vector c, as will be discussed in detail below. However, it is notnecessary to calculate the intercept parameter b in order to generate amass flow estimate. Equation (2) can be rewritten as:

X _(e) =Y _(e) a  (5)

using no intercept parameter b. Equation (5) may be viewed as an attemptto match the shape of the time difference estimate vector X_(e) to theshape of the reference time difference vector Y_(e) without accountingfor phase normalization. Equation (5) may work if the time differenceestimate vector Y_(e) and the reference time difference vector X_(e) arearbitrarily normalized, and may produce better results if all of thephases are normalized by the reference phase before determination of thetime difference estimates X_(e). To solve for the slope parameter a, thefollowing relation may be used:

a=Y _(e) ⁻¹ X _(e).  (6)

FIG. 11 illustrates operations 1100 for generating a mass flow estimatewithout determining the intercept parameter b according to embodimentsof the present invention. A pseudoinverse Y_(e) ⁻¹ of vector ofreference time differences Y_(e) associated with a known mass flow F_(c)is determined (Block 1110). The determination of the pseudoinverse Y_(e)⁻¹ may be done on an intermittent basis, e.g., at calibration, to reducecomputational burdens. The vector of time difference estimates X_(e) ismultiplied by the pseudoinverse Y_(e) ⁻¹ to determine a slope parametera (Block 1120). The slope parameter a is then multiplied by the knownmass flow F_(c) to produce a mass flow estimate (Block 1130). It will beappreciated that the mass flow estimate may be further processed; forexample, the mass flow estimate may be averaged with other mass flowestimates determined over a time period to produce a filtered mass flowmeasurement (Block 1140).

FIGS. 12 and 13 graphically illustrate test results for a prototypeCoriolis mass flowmeter according to embodiments of the invention thatindicate that determination of the intercept parameter b is not neededto generate mass flow estimates. In particular, FIGS. 12 and 13illustrates that mass flow estimates generated over time intervals ofinterest (approximately 10 to approximately 30 seconds) using respectiveones of the pseudoinverse methods described above (i.e., with andwithout determination of the intercept parameter b, respectively ) showa similar degree of agreement with experimental mass flow ratemeasurements for the time intervals obtained using other means.

According to other embodiments of the present invention, a iterativetechnique may be used to solve for the vector c in place of thepseudoinverse techniques described above. An error equation

L(k)=X _(e)(k)−Zc(k−1),  (7)

and an associated cost function $\begin{matrix}{J = {\frac{1}{2}L^{2}}} & (8)\end{matrix}$

can be defined. A gradient method can be used to find a solution thatreduces the cost function J to a desired level, with the gradient givenby: $\begin{matrix}{\frac{\partial J}{\partial c} = {- {{LZ}.}}} & (9)\end{matrix}$

Small steps may be taken down the gradient towards a minimum value ofthe cost function J. At a kth step, a new estimate of the vector c(k) isproduced using the following relation: $\begin{matrix}{{{c(k)} = {{{c\left( {k - 1} \right)} - {\gamma \frac{\partial J}{\partial c}}} = {{c\left( {k - 1} \right)} + {\gamma \quad {LZ}}}}},} & (10)\end{matrix}$

where the vector c(k−1) represents the result produced by the precedingk−1 iteration and γ is an adaptive rate for the process. Computationsmay be repeatedly performed until the cost function J is reduced to apredetermined level. γ should be greater than zero and less than 2 toensure convergence. The value of γ generally impacts the rate ofconvergence and the sensitivity of the iterative process to noise.Generally, the larger the value of γ, the faster the process converges;however, a large value for γ may increase sensitivity to noise. Anoptimum value for γ may be determined experimentally, which a typicallyvalue being 0.1.

Equation (10) represents a Least Mean Square (LMS) approach to parameterestimation. A potentially more robust Normalized Least Mean Square(NLMS) version of this adaptive approach may also be used as follows:$\begin{matrix}{{{c(k)} = {{c\left( {k - 1} \right)} - {\gamma \quad \frac{Z^{T}{L(k)}}{\alpha + {Z}_{2}^{2}}}}},} & (11)\end{matrix}$

where

0<γ<2  (12),

and α is a constant that is included to reduce the likelihood ofnumerical instability if the norm of Z approaches zero. In order toprovide convergence for equation (11), equation (12) should besatisfied. The value of a preferably is a small positive value and maybe selected based on experimentation.

FIG. 14 illustrates operations 1400 according to embodiments of thepresent invention, in which a scaling vector c is iteratively determinedalong the lines described above. A vector X_(e) of time differenceestimates is generated (Block 1410). An initial scaling vector estimatec(k) is generated (Block 1420). The initial value c(k) may be, forexample, zero or a final estimate of a scaling vector c generated from aprevious value of X_(e). Assuming that flow rate does not changedrastically between flow measurements, the latter choice may increasethe speed of convergence, as the previously estimated value for thescaling vector c should be close to the new value to be determined. Anassociated error L(k) and cost J(k) are determined, e.g., usingequations (7) and (8) (Block 1440). If the cost J(k) is less than apredetermined value, indicating an acceptable accuracy of the scalingvector estimate c(k), an estimate of mass flow may be generated (Blocks1450, 1455) and a new vector of time difference estimates X_(e)generated (Block 1410). If not, an updated estimate of the scalingvector c(k) is generated using, for example, equation (10) or equation(11) (Blocks 1460, 1470), and new error and cost function values arecomputed (Blocks 1430, 1440).

Those skilled in the art will appreciate that operations other thanthose described with reference to FIG. 14 may be used with the presentinvention. For example, it will be appreciated that many of thecomputations may be combined or varied. It will also be appreciated thatthere are many different iterative techniques that can be used to solveequation (3) beyond the LMS and NLMS techniques described above.

FIGS. 15-19 are flowchart illustrations of exemplary operationsaccording to various embodiments of the present invention. Those skilledin the art will understand that the operations of these flowchartillustrations may be implemented using computer instructions. Theseinstructions may be executed on a computer or other data processingapparatus, such as the data processor 450 of FIG. 4, to create anapparatus (system) operative to perform the illustrated operations. Thecomputer instructions may also be stored as computer readable programcode on a computer readable medium, for example, an integrated circuitmemory, a magnetic disk, a tape or the like, that can direct a computeror other data processing apparatus to perform the illustratedoperations, thus providing means for performing the illustratedoperations. The computer readable program code may also be executed on acomputer or other data-processing apparatus to cause the apparatus toperform a computer-implemented process. Accordingly, FIGS. 15-19 supportapparatus (systems), computer program products and methods forperforming the operations illustrated therein.

According to embodiments of the present invention illustrated by FIG.15, operations 1500 for generating phase estimates associated withmotion of a structure include mode selective filtering a plurality ofmotion signals representing motion of the structure to generate acorresponding plurality of mode selective filtered motion signals using,for example, techniques such as those described above with reference toFIG. 6. (Block 1510). A plurality of phase estimates is then generatedfrom the plurality of mode selective filtered motion signals (Block1520).

In exemplary mass flow estimation operations 1600 according toembodiments of the present invention illustrated in FIG. 16, a pluralityof motion signals representing motion of a conduit are mode selectivefiltered to produce a plurality of mode selective filtered motionsignals (Block 1610). A plurality of phase estimates is then generatedfrom the plurality of mode selective filtered motion signals (Block1620), and is used to generate a mass flow estimate (Block 1630).

In exemplary difference estimation operations 1700 according to otherembodiments of the present invention illustrated in FIG. 17, a pluralityof motion signals representing motion of a structure are mode selectivefiltered to produce a plurality of mode selective filtered motionsignals (Block 1710). A frequency of a first mode selective filteredmotion signal is determined using, for example, the adaptive notchfiltering operations described above with reference to FIG. 7 (Block1720). A difference estimate, e.g., a phase difference estimate and/or atime difference estimate, is then determined from a second modeselective filtered motion signal using, for example, the demodulationoperations described with reference to FIG. 7. (Block 1730).

FIG. 18 illustrates Operations 1800 for generating a mass flow estimateaccording to yet other embodiments of the present invention. A pluralityof motion signals representing motion of a conduit are processed togenerate a plurality of difference estimates, for example, timedifference estimates or phase difference estimates (Block 1810). A slopeparameter relating the plurality of difference estimates to a pluralityof reference difference values corresponding to a known mass flow isthen estimated (Block 1820), and a mass flow estimate is generated fromthe estimated slope parameter and the known mass flow (Block 1830).These operations may be implemented using, for example, the operationsdescribed above with reference to FIGS. 10 and 1.

In exemplary density estimation operations 1900 according to otherembodiments of the present invention illustrated in FIG. 19, a modaltransformation is applied to a plurality of motion signals representingmotion of a material-containing vessel to generate at least one modalmotion signal representing corresponding motion in a modal domaindefined by at least one vibrational mode of the vessel (Block 1910). Atleast one mode frequency is then determined from the at least one modalmotion signal (Block 1920), and a density of the material in the vesselis determined from the at least one mode frequency estimate (Block1930), for example, as described above with reference to FIG. 6.

Monitoring of Spatial Intercept or Other Correlation Measures to DetectSystem Status

As mentioned above with reference to FIGS. 10 and 11, although theintercept parameter b of the scaling vector c is not needed for massflow estimation, it may be useful for detecting system changes, such asmotion transducer failure, changes in mounting conditions and the like.Potential usefulness of the intercept parameter is illustrated by thegraphs of FIGS. 20A-20B and 21. FIGS. 20A-20B graphically illustratessimulated changes in computed mass flow rate and spatial interceptparameter, respectively, for failures of a motion transducer atapproximately 20 seconds, the failure of particular transducer beingsimulated by zeroing out the corresponding elements in the vectors oftime difference estimates produced by the transducer. As shown in FIG.20A, loss of a transducer produces a change in computed mass flow rate,which might be erroneously interpreted as an actual change in mass flowrate.

The change in the intercept parameter may be used, according toembodiments of the present invention, to trigger a fault correctionscheme. For example, as shown in FIGS. 20A and 20B, the pseudoinverse Wof an augmented matrix Z may be recalculated by striking the rowcorresponding to the failed transducer, and then used to generate newmass flow estimates. As shown in FIG. 20A, where such a correction isimplemented for mass flow estimates beginning at approximately 40seconds, improved accuracy may be achieved. In particular, for theexample shown, an error of 0.5% is achieved with such a correction incomparison to the 4% error occurring without such a correction.

As shown in FIG. 21, which illustrates intercept parameter values forfailures of each member of a group of five motion transducers, failuresof a motion transducer may be signaled by a corresponding large changein the intercept parameter, a phenomenon which typically would not occurin response to a mere change in mass flow. Other system changes, such aschanges in mounting or other conditions, may also be identified bychanges in the intercept parameter. In particular, FIG. 22 illustrateschanges in the intercept parameter for a prototype Coriolis mass flowmeter after damping is added to the structure of the meter.

The intercept parameter is one of a variety of different correlationmeasures that may be used to detect system changes according toembodiments of the present invention. In general, once a scaling vectorc has been calculated, equation (3) above can be applied to give avector of time differences X_(est), which is a least square fit of a“measured” vector of time differences X_(e) (produced as describedabove) to a basis vector:

X _(est) =Zc.  (13)

The predicted vector of time differences X_(est) may be compared to themeasured vector of time difference estimates X_(e) to produce acorrelation measure that can be used for various purposes. Thecomparison can be done intermittently or at each computation of massflow.

In embodiments of the present invention, a coefficient of correlation rmay generated from the predicted vector of time differences X_(est) andused to detect system changes. The coefficient of correlation r is adimensionless scalar quantity between +1 and −1, and uses a quantity{overscore (X)}, which is an average of the time difference estimatesX_(e): $\begin{matrix}{{\overset{\_}{X} = {{{mean}\left( X_{e} \right)} = {\sum\limits_{i = 1}^{N}\frac{X_{ei}}{N}}}},} & (14)\end{matrix}$

where N is the number of data points, e.g., the number of motiontransducer signals. The correlation coefficient r may be defined as aratio of explained variation over total variation: $\begin{matrix}{R = {{\pm \sqrt{\frac{explainedvariation}{totalvariation}}} = {\pm {\sqrt{\frac{\sum\left( {X_{est} - \overset{\_}{X}} \right)^{2}}{\sum\left( {X_{e} - \overset{\_}{X}} \right)^{2}}}.}}}} & (15)\end{matrix}$

FIG. 23 illustrates how such a correlation coefficient may be used, inparticular, in detecting transducer failure. Mass flow is estimated overa first time period of 0 to 15 seconds using vectors X_(e) of timedifference estimates generated from motion signals produced bytransducers #1-#5. Subsequently produced vectors X_(e) of timedifference estimates are then perturbed by zeroing out motion signalvalues corresponding to one motion transducer (#2) from 15 to 30seconds, simulating failure of that transducer for that time period.Vectors X_(e) of time difference estimates are again perturbed from 45to 60 seconds by doubling the motion signal value associated with the #2transducer, simulating a gain change in the transducer or a “noisy”transducer signal. As seen in FIG. 23, the mass flow estimate is reducedapproximately 20 lbm/min low when the #2 transducer input is zeroed andincreased approximately 15 lbm/min with the motion signal input doubled.

With standard flow measurement techniques, it may be difficult to tellwhether such changes are attributable to actual mass flow changes ormeasurement failures. However, in a manner similar to that describedabove with reference to the intercept parameter, the correlationcoefficient r may be used to detect such system changes. As shown inFIG. 24, which illustrates behavior of the correlation coefficient rover the same time interval as FIG. 23, the correlation coefficient rmay show a relatively large change in value with a failed (zeroed) ornoisy motion signal.

Error of estimate is another correlation measure that may be used fordetecting system status. A standard error of estimate s_(x,y) may beexpressed as: $\begin{matrix}{s_{x,y} = \sqrt{\frac{\sum\left( {X_{e} - X_{est}} \right)^{2}}{N}}} & (16)\end{matrix}$

As shown in FIG. 25, which shows behavior of the standard error ofestimate s_(x,y) for the time interval of FIGS. 23 and 24, the standarderror of estimate s_(x,y) may exhibit large changes for the systemchanges described above (it will be noted that sampling theory indicatesthat for a small number of transducer inputs (e.g., 6), greater accuracymay be achieved by replacing the N in the denominator with N−2.)

Other properties of the error of estimate measure can be exploited todetermine the source of a failure, such as the identity of a particularfailed transducer. The standard error of estimate may be viewed as beinganalogous to the standard deviation of a data set, i.e., one can expectthat 99.7% of the time, the error of estimate for a time differenceestimate will be within three times the standard error estimate s_(x,y)of the predicted vector of time differences X_(est). Accordingly, therespective errors of estimate for respective time difference estimatesassociated with respective transducers can be checked to see if they arewithin a predetermined multiple (e.g., within three times) of thestandard error of the estimate. Such a test may be expressed as thefollowing inequality:

X _(est) −K*s _(x,y) ≦X _(e) ≦X _(est) +K* s _(x,y),  (17)

which can be rearranged to give:

−K*S _(x,y) ≦X _(e) −X _(est) ≦+K* s _(x,y)  (18).

To identify a failed transducer, for example, the criterion of equations(17) and (18) can be applied to each component of each generated vectorof time difference estimates. An error (X_(e)−X_(est)) of a particulartime difference estimate X_(e) associated with a failed transducer willtypically be many times the standard error of estimate. This isillustrated in FIG. 26, which shows error (X_(e)-X_(est)) for a failedtransducer #2 of a group of transducers in relation to the standarderror of estimate for the group (the values of which are normalized forconvenience by subtracting out a nominal vector). As shown, the errorassociated with transducer #2 is well outside the standard error ofestimate bounds for the group (which, for the example shown, isapproximately ±0.07, too small to be seen on the plot of FIG. 26).

It is also possible to correct the computed mass flow rate for a failedtransducer once it has been identified. For example, the augmentedmatrix Z may be reformulated by deleting the row associated with thefailed transducer. A new pseudoinverse matrix W may then be formed byinverting the reformulated augmented matrix Z. Mass flow rate may thenbe estimated premultiplying a reduced dimension vector of timedifference estimates X_(e) in which the row associated with the failedtransducer by the new pseudoinverse matrix W is zeroed out. FIG. 27illustrates such correction of a mass flow rate estimate.

According to embodiments of the present invention, a flowmeter apparatusmay monitor an intercept parameter, correlation coefficient, standarderror of estimate or other correlation measure to detect system status.For example, upon detection of a large change in the interceptparameter, a particular failed transducer may be identified and themodal selective filter and/or the pseudoinverse matrix used by theapparatus to generate difference estimates may be recomputed tocompensate for the failed transducer. Similarly, an error of a timedifference estimate associated with a particular transducers movingoutside of a range defined by a standard error of estimate may be usedto detect transducer failure, and thus trigger corrective action.

FIG. 28 illustrates operations 2800 for detecting system statusaccording to embodiments of the present invention. A plurality ofdifference estimates, e.g., a vector of time difference estimates X_(e)as described above, is generated (Block 2810). A correlation measure,such as an intercept parameter, a correlation coefficient or an error ofestimate is determined (Block 2820). System status is determined fromthe determined correlation measure (Block 2830).

FIG. 29 illustrates exemplary operations 2900 according to otherembodiments of the present invention. A vector of time differenceestimates X_(e) is generated (Block 2910). A correlation measure, suchas an intercept parameter, a correlation coefficient or an error ofestimate, is determined (Block 2920). If a change in the correlationmeasure meets a predetermined criterion, a failed transducer isidentified (Blocks 2930, 2940). After identifying the failed transducer,appropriate elements of the augmented matrix Z may be zeroed out, andthe pseudoinverse matrix W may be recomputed for use in subsequent massflow and other computations (Blocks 2950, 2960, 2910). In this manner,input from the failed transducer may be excluded from subsequent massflow estimates.

Other corrective action may be taken based on a correlation measure. Forexample, in exemplary operations 3000 according to embodiments of thepresent invention illustrated in FIG. 30, an intercept parameter ismonitored (Block 3010) and, if a change in the intercept parameter meetsa predetermined criterion, the apparatus may recompute the modeselective filter it uses in generating mass flow estimates (Blocks 3020,3030). A variety of change criteria may be used, such as criteria basedon maximum deviation of the intercept parameter from an initial value,average deviation of the intercept parameter over a predetermined timeinterval, and the like.

Those skilled in the art will appreciate that the present invention maybe implemented a number of other ways than the embodiments describedherein. For example, computations described herein may be implemented asseparate computations, or may be combined into one or more computationsthat achieve equivalent results. The functions described herein may, ingeneral, be implemented using digital and/or analog signal processingtechniques. Those skilled in the art will also appreciate that, althoughthe present invention may be embodied within an apparatus such as aCoriolis mass flowmeter, or as methods which may be performed by suchapparatus, the present invention may also be embodied in a apparatusconfigured to operate in association with a flowmeter or sensorapparatus, such as in process control apparatus. It will also beappreciated that the present invention may be embodied in an article ofmanufacture in the form of computer-readable instructions or programcode embodied in a computer readable storage medium such as a magneticdisk, integrated circuit memory device, magnetic tape, bubble memory orthe like. Such computer program code may be executed by a computer orother data processor and executed responsive to motion signals suppliedfrom motion transducers operatively associated with a structure, such asa conduit or other vessel.

In the drawings and specification, there have been disclosed typicalpreferred embodiments of the invention and, although specific terms areemployed, they are used in a generic and descriptive sense only and notfor purposes of limitation, the scope of the invention being set forthin the following claims.

That which is claimed is:
 1. A method of estimating mass flow of amaterial in a conduit, the method comprising the steps of: modeselective filtering a plurality of motion signals representing motion ofthe conduit to generate a plurality of mode selective filtered motionsignals such that the mode selective filtered motion signalspreferentially represent motion associated with a vibrational mode ofthe conduit; generating a plurality of phase estimates from theplurality of mode selective filtered motion signals; and generating amass flow estimate from the plurality of phase estimates.
 2. A methodaccording to claim 1, wherein said step of generating a plurality ofphase estimates comprises the step of generating the plurality of phaseestimates using a phase reference derived from one of the plurality ofmode selective filtered motion signals.
 3. A method according to claim1, wherein said step of applying a mode selective filter comprises thesteps of: applying a modal transformation to the plurality of motionsignals to generate a plurality of modal response signals in a modalcoordinate domain; and applying a mode selective transformation to theplurality of modal response signals to generate the plurality of modeselective filtered motion signals.
 4. A method according to claim 1,wherein said step of generating a plurality of phase estimates comprisesthe steps of: estimating a frequency of a mode selective filtered motionsignal of the plurality of mode selective filtered motion signals;generating quadrature first and second reference signals based on theestimated frequency; and generating the plurality of phase estimatesfrom the plurality of mode selective filtered motion signals and thefirst and second reference signals.
 5. A method according to claim 4,wherein said step of generating the plurality of phase estimates fromthe plurality of mode selective filtered motion signals and the firstand second reference signals comprises the steps of: multiplying a modeselective filtered motion signal by respective ones of the first andsecond reference signals to generate respective real and imaginarycomponent signals of the mode selective filtered motion signal; andestimating an arctangent of a quotient of the real and imaginarycomponent signals of the mode selective filtered motion signal togenerate a phase estimate.
 6. A method according to claim 1, whereinsaid step of generating a mass flow estimate comprises the steps of:generating a plurality of time difference estimates from the pluralityof phase estimates; and generating the mass flow estimate from theplurality of time difference estimates.
 7. A method according to claim6, wherein said step of generating a plurality of time differenceestimates from the plurality of phase estimates comprises the step ofdividing the plurality of phase estimates by a mode frequency togenerate a plurality of time difference values.
 8. A method according toclaim 7, wherein said step of generating a plurality of time differenceestimates from the plurality of phase estimates further comprises thestep of applying a plurality of zero-flow reference time differences tothe plurality of time difference values to generate the plurality oftime difference estimates.
 9. A method according to claim 7, whereinsaid step of generating a plurality of time difference estimates fromthe plurality of phase estimates comprises correcting the plurality ofphase estimates using a plurality of zero flow phase values.
 10. Amethod according to claim 7, wherein said step of mode selectivefiltering comprises the step of applying a modal transformation to theplurality of motion signals to generate a modal motion signal in a modalcoordinate domain, and wherein the method further comprises the step ofestimating the mode frequency from the modal motion signal.
 11. A methodaccording to claim 10, further comprising the step of estimating densityof material in the conduit from the estimated mode frequency.
 12. Amethod according to claim 6, wherein said step of estimating mass flowfrom the plurality of time difference estimates comprises the steps of:estimating a slope parameter of a scaling function that relates theplurality of time difference estimates to a plurality of reference timedifferences representing motion of the conduit at a known mass flow; andgenerating a mass flow estimate from the estimated slope parameter andthe known mass flow.
 13. A method according to claim 12, wherein saidstep of estimating a slope parameter comprises the step of multiplyingthe plurality of time difference estimates by a pseudoinverse of theplurality of reference time differences to estimate the slope parameter.14. A method according to claim 12, wherein said step of estimating aslope parameter comprises the steps of: generating an augmented matrixincluding the plurality of reference time differences; and multiplyingthe plurality of time difference estimates by a pseudoinverse of theaugmented matrix to determine the slope parameter.
 15. A methodaccording to claim 12, wherein said step of estimating a slope parametercomprises the step of iteratively estimating the scaling function.
 16. Amethod according to claim 15, wherein said step of iterativelyestimating comprises the step of applying a Least Mean Square (LMS)estimation procedure.
 17. A method according to claim 12, wherein saidstep of estimating a slope parameter is preceded by the step ofprocessing a plurality of motion signals representing motion of theconduit at the known mass flow to generate the plurality of referencetime differences.
 18. A method according to claim 12, further comprisingthe step of estimating an intercept parameter of the scaling function.19. A method according to claim 18, further comprising the step ofdetermining a system status from the intercept parameter.
 20. Anapparatus, comprising: a conduit configured to contain a material; aplurality of motion transducers operatively associated with the conduitand operative to produce a plurality of motion signals representingmotion of the conduit; and a signal processing circuit that receives theplurality of motion signals, mode selective filters the plurality ofmotion signals to generate a plurality of mode selective filtered motionsignals such that the mode selective filtered motion signalspreferentially represent motion associated with a vibrational mode ofthe conduit, generates a plurality of phase estimates from the pluralityof mode selective filtered motion signals, and generates a mass flowestimate from the plurality of phase estimates.
 21. An apparatusaccording to claim 20, wherein the signal processing circuit generatesthe plurality of phase estimates using a phase reference derived fromone of the plurality of mode selective filtered motion signals.
 22. Anapparatus according to claim 20, wherein the signal processing circuitapplies a modal transformation to the plurality of motion signals togenerate a plurality of modal response signals in a modal coordinatedomain and applies a mode selective transformation to the plurality ofmodal motion signals to generate the plurality of mode selectivefiltered motion signals.
 23. An apparatus according to claim 20, whereinthe signal processing circuit estimates a frequency of a mode selectivefiltered motion signal of the plurality of mode selective filteredmotion signals, generates quadrature first and second reference signalsbased on the estimated frequency, and generates the plurality of phaseestimates from the plurality of mode selective filtered motion signalsand the first and second reference signals.
 24. An apparatus accordingto claim 20, wherein the signal processing circuit generates a pluralityof time difference estimates from the plurality of phase estimates andgenerates the mass flow estimate from the plurality of time differenceestimates and an estimated mode frequency.
 25. An apparatus according toclaim 24, wherein the signal processing circuit applies a plurality ofzero-flow reference time differences to the plurality of time differencevalues to generate the plurality of time difference estimates.
 26. Anapparatus according to claim 24, wherein the signal processing circuitapplies a modal transformation to the plurality of motion signals togenerate a modal motion signal in a modal coordinate domain, andestimates the mode frequency from the modal motion signal.
 27. Anapparatus according to claim 26, wherein the signal processing circuitestimates density of material in the conduit from the estimated modefrequency.
 28. An apparatus according to claim 24, wherein the signalprocessing circuit estimates a slope parameter of a scaling functionthat relates the plurality of time difference estimates to a pluralityof reference time differences representing motion of the conduit at aknown mass flow and generates the mass flow estimate from the estimatedslope parameter and the known mass flow.
 29. An apparatus according toclaim 28, wherein the signal processing circuit multiplies the pluralityof time difference estimates by a pseudoinverse of the plurality ofreference time differences to estimate the slope parameter.
 30. Anapparatus according to claim 28, wherein the signal processing circuitgenerates an augmented matrix including the plurality of reference timedifferences and multiplies the plurality of time difference estimates bya pseudoinverse of the augmented matrix to determine the slopeparameter.
 31. An apparatus according to claim 28, wherein the signalprocessing circuit iteratively estimates the scaling function.
 32. Anapparatus according to claim 28, wherein the signal processing circuitis operative to process a plurality of motion signals representingmotion of the conduit at the known mass flow to generate the pluralityof reference time differences.
 33. An apparatus according to claim 28,wherein the signal processing circuit is further operative to estimatean intercept parameter of the scaling function and to determine a systemstatus from the intercept parameter.
 34. An apparatus for processing aplurality of motion signals representing motion of a material-containingconduit, the apparatus comprising: means for mode selective filteringthe plurality of motion signals to generate a plurality of modeselective filtered motion signals such that the mode selective filteredmotion signals preferentially represent motion associated with avibrational mode of the conduit; means for generating a plurality ofphase estimates from the plurality of mode selective filtered motionsignals; and means for generating a mass flow estimate from theplurality of phase estimates.
 35. An apparatus according to claim 34,wherein the means for generating a plurality of phase estimatescomprises means for generating the plurality of phase estimates using aphase reference derived from one of the plurality of mode selectivefiltered motion signals.
 36. An apparatus according to claim 34, whereinthe means for applying a mode selective filter comprises: means forapplying a modal transformation to the plurality of motion signals togenerate a plurality of modal response signals in a modal coordinatedomain; and means for applying a mode selective transformation to theplurality of modal response signals to generate the plurality of modeselective filtered motion signals.
 37. An apparatus according to claim34, wherein the means for generating a plurality of phase estimatescomprises: means for estimating a frequency of a mode selective filteredmotion signal of the plurality of mode selective filtered motionsignals; means for generating quadrature first and second referencesignals based on the estimated frequency; and means for generating theplurality of phase estimates from the plurality of mode selectivefiltered motion signals and the first and second reference signals. 38.An apparatus according to claim 37, wherein the means for generating theplurality of phase estimates from the plurality of mode selectivefiltered motion signals and the first and second reference signalscomprises: means for multiplying a mode selective filtered motion signalby respective ones of the first and second reference signals to generaterespective real and imaginary component signals of the mode selectivefiltered motion signal; and means for estimating an arctangent of aquotient of the real and imaginary component signals of the modeselective filtered motion signal to generate a phase estimate.
 39. Anapparatus according to claim 34, wherein the means for generating a massflow estimate comprises: means for generating a plurality of timedifference estimates from the plurality of phase estimates; and meansfor generating the mass flow estimate from the plurality of timedifference estimates.
 40. An apparatus according to claim 39, whereinthe means for generating a plurality of time difference estimates fromthe plurality of phase estimates comprises the means for dividing theplurality of phase estimates by a mode frequency to generate a pluralityof time difference values.
 41. An apparatus according to claim 40,wherein the means for generating a plurality of time differenceestimates from the plurality of phase estimates further comprises meansfor applying a plurality of zero-flow reference time differences to theplurality of time difference values to generate the plurality of timedifference estimates.
 42. An apparatus according to claim 34, whereinthe means for mode selective filtering comprises means for applying amodal transformation to the plurality of motion signals to generate amodal motion signal in a modal coordinate domain, and wherein theapparatus further comprises means for estimating the mode frequency fromthe modal motion signal.
 43. An apparatus according to claim 42, furthercomprising means for estimating density of material in the conduit fromthe estimated mode frequency.
 44. An apparatus according to claim 40,wherein the means for estimating mass flow from the plurality of timedifference estimates comprises: means for estimating a slope parameterof a scaling function that relates the plurality of time differenceestimates to a plurality of reference time differences representingmotion of the conduit at a known mass flow; and means for generating amass flow estimate from the estimated slope parameter and the known massflow.
 45. An apparatus according to claim 44, wherein the means forestimating a slope parameter comprises means for multiplying theplurality of time difference estimates by a pseudoinverse of theplurality of reference time differences to estimate the slope parameter.46. An apparatus according to claim 44, wherein the means for estimatinga slope parameter comprises: means for generating an augmented matrixincluding the plurality of reference time differences; and means formultiplying the plurality of time difference estimates by apseudoinverse of the augmented matrix to determine the slope parameter.47. An apparatus according to claim 44, wherein the means for estimatinga slope parameter comprises means for iteratively estimating the scalingfunction.
 48. An apparatus according to claim 47, wherein the means foriteratively estimating comprises means for applying a Least Mean Square(LMS) estimation procedure.
 49. An apparatus according to claim 44,further comprising means for processing a plurality of motion signalsrepresenting motion of the conduit at the known mass flow to generatethe plurality of reference time differences.
 50. An apparatus accordingto claim 44, further comprising means for estimating an interceptparameter of the scaling function.
 51. An apparatus according to claim50, further comprising means for determining a system status from theintercept parameter.
 52. A computer program product for estimating massflow of a material in a conduit, the computer program productcomprising: a computer-readable storage medium having computer-readableprogram code embodied in the computer-readable storage medium, thecomputer-readable program code comprising: mass flow estimatingcomputer-readable program code that mode selective filters a pluralityof motion signals representing motion of the conduit to generate aplurality of mode selective filtered motion signals such that the modeselective filtered motion signals preferentially represent motionassociated with a vibrational mode of the conduit, that generates aplurality of phase estimates from the plurality of mode selectivefiltered motion signals, and that generates a mass flow estimate fromthe plurality of phase estimates.
 53. A computer program productaccording to claim 52, wherein the mass flow estimatingcomputer-readable program code generates the plurality of phaseestimates using a phase reference derived from one of the plurality ofmode selective filtered motion signals.
 54. A computer program productaccording to claim 52, wherein the mass flow estimatingcomputer-readable program code estimates a frequency of a mode selectivefiltered motion signal of the plurality of mode selective filteredmotion signals, generates quadrature first and second reference signalsbased on the estimated frequency, and generates the plurality of phaseestimates from the plurality of mode selective filtered motion signalsand the first and second reference signals.
 55. A computer programproduct according to claim 52, wherein the mass flow estimatingcomputer-readable program code generates a plurality of time differenceestimates from the plurality of phase estimates and generates the massflow estimate from the plurality of time difference estimates.
 56. Acomputer program product according to claim 55, wherein the mass-flowestimating computer-readable program code applies a modal transformationto the plurality of motion signals to generate a modal motion signal ina modal coordinate domain, and estimates a mode frequency from the modalmotion signal, and generates the plurality of time difference estimatesfrom the plurality of phase estimates using the estimated modefrequency.
 57. A computer program product according to claim 56, whereinthe computer-readable program code further comprises density estimatingcomputer-readable program code that estimates density of material in theconduit from the estimated mode frequency.